What is the integral from 1 to 2 of (x+1)/(sqrt(x)) ?

The integral from 1 to 2 of (x+1)/(sqrt(x)) is (4sqrt(2)-2)/3+2sqrt(2)-2

Popular >

integral from 1 to 2 of (x+1)/(sqrt(x))

\int_{1}^{2} \frac{x + 1}{x} d x

\frac{4 2 - 2}{3} + 22 - 2

Decimal Notation

2.04737 \dots

Solution steps

\int_{1}^{2} \frac{x + 1}{x} d x

Expand

\frac{x + 1}{x} : x + \frac{1}{x}

= \int_{1}^{2} x + \frac{1}{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{2} x d x + \int_{1}^{2} \frac{1}{x} d x

\int_{1}^{2} x d x = \frac{4 2 - 2}{3}

\int_{1}^{2} \frac{1}{x} d x = 22 - 2

= \frac{4 2 - 2}{3} + 22 - 2

\frac{d ^{4} y}{d x ^{4}} - 23 \frac{d ^{2} y}{d x ^{2}} - 50 y = 0

5 x + \frac{4}{x}

x \to 0 lim (- (\frac{1}{x} - \frac{1}{∣ x ∣}))

x \to 0 lim (sin (2 x))

\frac{d}{d y} (- \frac{y}{x ^{2} + y ^{2}})

What is the integral from 1 to 2 of (x+1)/(sqrt(x)) ?
The integral from 1 to 2 of (x+1)/(sqrt(x)) is (4sqrt(2)-2)/3+2sqrt(2)-2